erweitern ((2x-3)(3y+2x))/(2xy)

Lösung

erweitern

\frac{( 2 x - 3 ) ( 3 y + 2 x )}{2 x y}

3 + \frac{2 x}{y} - \frac{9}{2 x} - \frac{3}{y}

Schritte zur Lösung

\frac{( 2 x - 3 ) ( 3 y + 2 x )}{2 x y}

Multipliziere aus

(2 x - 3) (3 y + 2 x) : 6 x y + 4 x^{2} - 9 y - 6 x

= \frac{6 x y + 4 x ^{2} - 9 y - 6 x}{2 x y}

Wende Bruchregel an:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{6 x y + 4 x ^{2} - 9 y - 6 x}{2 x y} = \frac{6 x y}{2 x y} + \frac{4 x ^{2}}{2 x y} - \frac{9 y}{2 x y} - \frac{6 x}{2 x y}

= \frac{6 x y}{2 x y} + \frac{4 x ^{2}}{2 x y} - \frac{9 y}{2 x y} - \frac{6 x}{2 x y}

\frac{6 x y}{2 x y} = 3

\frac{4 x ^{2}}{2 x y} = \frac{2 x}{y}

\frac{9 y}{2 x y} = \frac{9}{2 x}

\frac{6 x}{2 x y} = \frac{3}{y}

= 3 + \frac{2 x}{y} - \frac{9}{2 x} - \frac{3}{y}

e x p an d 4 x + 2 (4 - 2 = 20)

e x p an d 2 π (7 x + 6)

e x p an d (x^{2} + 3 x - 2) \cdot (ln (x))

e x p an d M (- 3, - 1)

e x p an d \frac{3}{( x + 2 ) ^{2} ( x - 3 ) ^{2}}